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201004.3424v1 Special values of L-functions and the arithmetic of Darmon points.pdf
- Building on our previous work on rigid analytic uniformizations, we introduce Darmon points on Jacobians of Shimura curves attached to quaternion algebras over Q and formulate conjectures about their rationality properties.
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Darmon and Rotger´s Graduate mini-course on the Birch and Swinnerton-Dyer conjecture in Moscow, September 2014.pdf
- 本迷你课程的目标为讨论Birch and Swinnerton Dyer（BSD）猜想。BSD猜想是数论中最著名的未完
全解决问题之一，也是克莱研究所的七个“千禧奖问题之一”。自60年初的成形以来，在BSD猜想的进
展来主要自以下几个方向：
1. Coates 与 Wiles在二十世纪七十年代后期的开创性工作，证明了该猜想成立的
第一种情形：具有复乘的椭圆曲线且解析秩为0。
2.二十世纪八十代，Zagier和kolyvagin的联合突破，导致所有的Q上模的椭圆曲
线在解析秩为0或1的情形下BSD猜想的证明；这种方法也给出了在虚二次域关于
他们的Mordell-Weil和Shafarevich-Tate 群强的信息。
3.二十世纪九十代由Kato的工作证明了BSD猜想的如下情形：解析秩为零且为Q上
的模椭圆曲线和分圆域上Mordell-Weil群。
4.最近几年来，Skinner 与 Urban更为现代的方法，该方法的灵感来自Mazur和
Wiles在分圆域算术的早期工作，导致了代数阶为0级时所有模椭圆曲线的BSD猜
想的证明，以及证明了Iwasawa理论在这种情形下的“主猜想”。
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Henri Darmon and Victor Rotger, Diagonal cycles and Euler systems II - the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-series.pdf
- This article establishes new cases of the Birch and Swinnerton-Dyer conjecture in analytic rank 0, for elliptic curves over Q viewed over the fields cut out by certain self-dual Artin representations of dimension at most 4. When the associated L-function vanishes (to even order2)
at its central point, two canonical classes in the corresponding Selmer group are constructed and shown to be linearly independent assuming the non-vanishing of a Garrett-Hida p-adic L-function at
a point lying outside its range of classical interpolation. The key tool for both results is the study of certain p-adic families of global Galois cohomology classes arising from Gross-Kudla-Schoen diagonal cycles in a tower of triple products of modular curves.
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A generalization of Darmon´s conjecture for Euler systems for general p-adic representations.pdf
- A generalization of Darmon´s conjecture for Euler systems for general p-adic representations
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10.1.1.228.6841 Diagonal cycles and Euler systems I - A p-adic Gross-Zagier formula by Henri Darmon , Victor Rotger.pdf
- 10.1.1.228.6841 Diagonal cycles and Euler systems I - A p-adic Gross-Zagier formula by Henri Darmon , Victor Rotger10.1.1.228.6841 Diagonal cycles and Euler systems I - A p-adic Gross-Zagier formula by Henri Darmon , Victor Rotger10.1.1.228.6841 Diagonal cycles and Euler systems I - A p-adic Gross-Zagier formula by Henri Darmon , Victor Rotger
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10.1.1.182.2714 Chow-Heegner points on CM elliptic curves and values of p-adic L-series (2010) by Massimo Bertolini , Henri Darmon , Kartik Prasanna.pdf
- 10.1.1.182.2714 Chow-Heegner points on CM elliptic curves and values of p-adic L-series (2010) by Massimo Bertolini , Henri Darmon , Kartik Prasanna10.1.1.182.2714 Chow-Heegner points on CM elliptic curves and values of p-adic L-series (2010) by Massimo Bertolini , Henri Darmon , Kartik Prasanna10.1.1.182.2714 Chow-Heegner points on CM elliptic curves and values of p-adic L-series (2010) by Massimo Bertolini , Henri Darmon , Kartik Prasanna
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overconvergent cohomology and quaternionic darmon strongpointsstrong.pdf
- overconvergent cohomology and quaternionic darmon strongpointsstrong
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L-INVARIANTS AND DARMON CYCLES ATTACHED TO.pdf
- L-INVARIANTS AND DARMON CYCLES ATTACHED TO —文档、资料、论文、办公、总结，均是精品资料，免费阅读，免费分享，值得下载！
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201307.2556v1 Computation of quaternionic p-adic Darmon points.pdf
- We give an overconvergent algorithm for the explicit computation of the quaternionic Darmon points introduced by M. Greenberg, and we provide the first numerical calculations that give empirical evidence of their rationality.
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向豆丁求助：有没有darmon?
